The point A(−10, 0) is on the ellipse with equation x^2/100+y^2/64 =1. What is the sum of the distances AF1 + AF2, where F1 and F2 are the foci?

Question

The point A(−10, 0) is on the ellipse with equation . What is the sum of the distances AF1 + AF2, where F1 and F2 are the foci?

a. 10

b. 12

c. 14

d. 20

Answer 1

The semi-major axis (a) is length 10 and semi-minor axis (b) is length 8 where the standard equation of the ellipse is:

x²/a²+y²/b²=1=x²/10²+y²/8²=1. A(-10,0) is on the x-axis at the left extremity of the ellipse a distance 'a' from the centre.

If f is the focal distance, then AF1=-f-(-10)=10-f (where F1 is the left focus) and AF2=10+f. So the sum is 10-f+10+f=20 (answer d), because the foci are at F1(-f,0) and F2(f,0).